Shortly after becoming mayor, former city officials and Wasilla residents said, Ms. Palin approached the town librarian about the possibility of banning some books, though she never followed through and it was unclear which books or passages were in question.

Ann Kilkenny, a Democrat who said she attended every City Council meeting in Ms. Palin’s first year in office, said Ms. Palin brought up the idea of banning some books at one meeting. “They were somehow morally or socially objectionable to her,” Ms. Kilkenny said.

The librarian, Mary Ellen Emmons, pledged to “resist all efforts at censorship,” Ms. Kilkenny recalled. Ms. Palin fired Ms. Emmons shortly after taking office but changed course after residents made a strong show of support. Ms. Emmons, who left her job and Wasilla a couple of years later, declined to comment for this article.